Most e-juice bottle unless you are carrying a quart sized bottles are smaller than the maximum allowed for carry on the allowed size are a few ounces like sample sized shampoos etc. I don't believe there is a max number of how many you can carry on, but certainly you culd get on with a bottle or two.
Couple of things I but in check through or not take at all if I am going strictly carry on are the large syringes with the blunt needles (or any needle for that matter unless you carry them for a medical reason like diabetes but diabetes aren't using 10 cc syringes and the TSA knows that. Obviously I don't carry there bottle with blunt needle tops either. I had some in my 'vape' case on one trip and was stopped and asked about them even though they were not on either syringes or bottle and I had neither with me (they had just gotten forgotten in the case). The TSA kindly tossed them for me to avoid further embarrassment.
I would not travel with DIY supplies, mix at home.To be homest for traceling I prefer purchased e-juice as I can get it with labels, my own in unlabeled bottles seems to raise questions about what is in there and how are they supposed to know but they never have questioned the labled one - just read them. Another reason for not DYO n a trip (besides the time) is that there are all sorts of regulations about transporting toxic substances on a plane in flight, whether in the cargo hold, luggage area or your lap, and nicotine base is that in a nutshell.
Just to make things simple if you are traveling with more than one battery, atty, charger and bottle of e-juice, get yourself a diabetic supplies case or makeup case and put it all in one place. Easier for them to zip open a case to inspect what is in there when they see it on the x-ray then digging through a backpack or bag and pulling it out piecemeal. I love the diabetes supply cases as there are a ton of size ranges, they have plenty of net and plastic pockets, velcro and elastic loops (just the right size for vaping supplies as diabetic supplies are often about the same size and shape. Most come with one pouch for what a diabetic would use for discarding lancets and test stripsa and other cataninates - nice for anything you might think will leak and get into everything else.
You can also place bottles back int the small ziplock baggies that your juice was in when shipped to you and place the juice in it before sliding into the straps. These cases are insulated and padded to keep diabetic supplies including glass items, electronic meters, etc safe so that protection is nice for your vaping supplies. These cases are not huge but can run from the size or an ego case to larger but hold much more than a battery, atty and charger. My case gets carried on with me, and the case provide great protection, the case stays near me, I know where my stuff is and it does not look awkward to the public.
Some come with cooling pack to keep them at a nice temp if traveling in hot weather. They are cushioned and usually have a clip or other mechanism that will hang on a belt or outside a backpack or bag and save space for things you want to put inside. Its a nice presentation and easy for them to look at without rummaging around in a pile. Cosmetic bags can work too if you get ones that have the various compartments and are long enough for batteries etc but since diabetes supplies usually entail the need to carry insulin pens a bit longer by same diameter as many insulin pens, insulin, other syringes, bottles of insulin (about the same diameter as juice bottles) and so on.
Since I have had the case (infact I have several depending on what I am taking and how long I will be gone) I have had pretty fast check thoughts; open the case like any other (laptop, carry on etc) and let the TSA ponder all my cool stuff and with what neatness I have it arranged, To be honest I think many think they re seeing diabetes supplies since they expect to with those cases and wouldn't know a PV from a flashlight. i guess it just depends on how much 'vaping' inservice they have had. Least I am not answering questions and holding up the line.
and I can't bear the thought of anything happening too it. I'm not worried about the TSA as much as the hustle bustle and hassle of travel. I'm afraid I'd lose it honestly. On my last business trip I left my mac power cord in the airport 
